Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
407 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 407 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10590301 | C2 | semidirect |
| 4. #10590259 | C2 | semidirect |
| 6. #10589100 | C2 | semidirect |
| 7. #10589094 | C2 | semidirect |
| 112. C3⋊(C3⋊C8) | SD16 | semidirect |
| 312. C32 | #1686 | semidirect |
| 359. C3 | #68412 | semidirect |
| 360. C3 | #71024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592775 | 2 |
| C3×#5075 | 2 |
| #10590301 | 2 |
| #10590259 | 2 |
| C3×#4544 | 2 |
| #10589100 | 2 |
| #10589094 | 2 |
| #71024 | 3 |
| #68412 | 3 |